If Luiz Suarez was good enough and other bla-bla-bla. Just admin that he is old for football already. He is where he is not because clubs can not afford him, or he has lack of skill, he is just old for football. Google say that football players retire at 34-38. Suarez is 36 already. Football players peak form is between 25-27. And Duelbits made a contract with him, because among famous and good players, Suarez is famous, good, but has that biting controversial feature.
As long as the player is no longer in peak physical shape, as you said, from the age of 25-27, in my opinion, it's not so simple to define whether you're old enough to play soccer
If the team has a good composition of young players and older and more experienced players, it can use the experience of a player of this size to its advantage. A player who has played in Europe, Champions League, against all the best teams in the world, the World Cup, etc., has a lot to add to a team
I've heard that usually peak performance for men is 33 but you can probably mitigate age related issues by training, sleeping and eating well, with some limitation, of course, as an example it'll be hard to see a 50 years old compete with a 25 who's in shape and practicing often.